Optimal. Leaf size=22 \[ \frac{2 \sqrt{5 x+3}}{11 \sqrt{1-2 x}} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0019502, antiderivative size = 22, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.053, Rules used = {37} \[ \frac{2 \sqrt{5 x+3}}{11 \sqrt{1-2 x}} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 37
Rubi steps
\begin{align*} \int \frac{1}{(1-2 x)^{3/2} \sqrt{3+5 x}} \, dx &=\frac{2 \sqrt{3+5 x}}{11 \sqrt{1-2 x}}\\ \end{align*}
Mathematica [A] time = 0.0033949, size = 22, normalized size = 1. \[ \frac{2 \sqrt{5 x+3}}{11 \sqrt{1-2 x}} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.002, size = 17, normalized size = 0.8 \begin{align*}{\frac{2}{11}\sqrt{3+5\,x}{\frac{1}{\sqrt{1-2\,x}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 3.83902, size = 28, normalized size = 1.27 \begin{align*} -\frac{2 \, \sqrt{-10 \, x^{2} - x + 3}}{11 \,{\left (2 \, x - 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.68095, size = 62, normalized size = 2.82 \begin{align*} -\frac{2 \, \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{11 \,{\left (2 \, x - 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 1.04421, size = 48, normalized size = 2.18 \begin{align*} \begin{cases} \frac{\sqrt{10}}{11 \sqrt{-1 + \frac{11}{10 \left (x + \frac{3}{5}\right )}}} & \text{for}\: \frac{11}{10 \left |{x + \frac{3}{5}}\right |} > 1 \\- \frac{\sqrt{10} i}{11 \sqrt{1 - \frac{11}{10 \left (x + \frac{3}{5}\right )}}} & \text{otherwise} \end{cases} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 2.60861, size = 35, normalized size = 1.59 \begin{align*} -\frac{2 \, \sqrt{5} \sqrt{5 \, x + 3} \sqrt{-10 \, x + 5}}{55 \,{\left (2 \, x - 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]